These flight management systems FMS are well known. They make it possible to generate the flight plan of an aircraft on each mission, taking account of the parameters specific to the aircraft and to the flight conditions such as the payload, the weight of the aircraft, the quantity of fuel onboard, the temperature, the wind etc., and of the time constraints imposed by the air traffic control bodies ATC: required departure and/or arrival timeslot.
The flight plan notably describes all the waypoints or positions above which the aircraft is to pass, with the altitude and corresponding speed at each waypoint. It supplies a vertical flight profile for the various phases of the aircraft, typically the climb phase CLB, the cruise phase CRZ and the descent phase DES, as illustrated schematically in simplified form in FIG. 1. Depending on this vertical profile, notably the speed over the ground and the cruising altitude correspond to each of the phases. The climb phase typically begins at the time tCLB to stop at the time tTOC, at the TOC (Top Of Climb) point at which the aircraft reaches cruising altitude ALTCRZ; the cruise phase extends between the time tTOC and the time tTOD, the latter corresponding to the TOD (Top of Descent) point at which the aircraft begins the descent DES to landing at the destination.
Flight management systems are more recently known that also use economic criteria, taking the form of a Cost Index CI. This cost index is in fact an optimization criterion between the Cost of Time CT in $/minute for example, and the Cost of Fuel CF in $/kg for example. The Cost Index is defined by CI=CT/CF, with normal values lying between 0 and 999 (in kg/minute with the units indicated above).
The value of this cost index for an aircraft and a given mission is determined according to criteria specific to each operator, and constrains notably the rules for determining the altitudes and speeds of the flight plan (vertical profile of the flight plan).
Typically, a cost index CI equal to zero corresponds to a situation in which the cost of time CT is considered to be negligible relative to the cost of fuel CF: planning the flight will consist in seeking speeds low enough to consume as little as possible, and the flight duration will thereby be longer. For an operator, this typically corresponds to flights of the long haul type.
A cost index CI equal to 999 corresponds to an opposite situation, in which the cost of fuel CF is considered to be negligible relative to the cost of time CT: planning the flight will consist in seeking the shortest flight duration, even if the consumption of fuel must be high. For an operator, this typically corresponds to flights of the shuttle type, to allow a maximum number of rotations, or else to ensure an earlier arrival time in case of lateness or of a precise landing slot.
In practice, a cost index is calculated by an operator:
by determining the cost of time CT: the operator includes the operating costs including notably, but not exclusively, the amortization of the machines and equipment, taxes included; the hourly salaries of the crews and of the duty staff; the flight taxes (on-route, airports, security, etc.) and the service expenses (weather forecasting, assistance, etc.); the cost of the connections impacted in management of computer networks central node (“hub” management); the cost of delays (hotel, passenger transfer and compensation, meals or meal compensations expenses, etc.); the cost of insurance; the cost of lateness (airport fire cover, standby duty/activation of controllers, security services, ground support) and taxes according to arrival times; aircraft maintenance (regular inspections); impact of crew hours (rest times, maximum monthly flying time, etc.).
by determining the cost of fuel CF: this involves the unit cost of fuel at the airport where the aircraft is filled up, which includes the cost of the fuel margins taken away.
For an operator, the cost index CI reflects the search to optimize the operating cost, as a function of the type of flight (medium range, long haul, shuttle, charter, etc.), that is to say an optimum between the cost of time and the cost of fuel. A flight management system FMS onboard an aircraft will compute the flight predictions for a given mission as a function of the data input by the pilot, including the optimum cost index CI determined by the operator for this flight, as a function of the parameters listed above. In this manner, an optimal flight plan according to the economic criteria of the operator is obtained.
However, during a mission, additional temporary constraints of air traffic management or constraints imposed by the crew, may cause the aircraft to depart from the optimal flight plan. In particular, an air traffic controller may notably:
modify the flight plan or give manual flight instructions of the “vector” type for matters of traffic management (resolution of conflicts, maintaining separation, sector optimization), of weather, of runway occupancy management on arrival, etc.
modify the speed of the aircraft for reasons of coordination, of separation between aircraft in a control sector or between adjacent control sectors;
impose a timetable constraint, of time, on a waypoint or a particular point of the flight plan, for example, on the destination point or the initial approach point: this imposes a cost index called the RTA (Required Time of Arrival), which is no longer an optimal index for the operator since it takes account of a constraint imposed by air traffic control ATC.
The flight parameters for a flight phase may also be modified by the crew for internal reasons, and by the air traffic controller for air traffic management reasons. For example:
the climb phase CLB may be modified for traffic reasons. For example, it is possible to impose the fastest possible climb to cruising level beginning at the top of climb point TOC;
the cruise phase CRZ may be modified for example to respond to constraints of optimizing fuel consumption (operating economy) or of managing the reserve of fuel on arrival: a different altitude and a slower cruising speed than the initially predicted altitude and speed may be imposed.
All these actions have the effect that the flight plan actually followed differs from the optimal flight plan: the initial optimal cost index of the operator that is one of the parameters for determining the optimal flight plan will not be maintained: the aircraft will arrive either too early or too late, with a quantity of fuel remaining onboard that is different from the optimal estimates.
In addition, the cost of time CT is normally considered to be a monotonic function of the time, as illustrated in FIG. 2a, whereas in reality the total cost of time CT of an aircraft for a given mission is a complex function G(t), as illustrated as an example in FIG. 2b. Specifically, depending on whether the aircraft arrives in the required arrival timeslot, or outside this timeslot, that is to say before or after, with a greater or lesser time difference, the consequences on the cost of time may in reality be very different. Notably it is possible to express this difference by a component ΔC of the cost of time which reflects the failure to adhere to the arrival timeslot required by air traffic management ATM. This component ΔC of non-adherence may in practice result in an increase or else a reduction in the total cost of time.
This component of non-adherence is illustrated in FIG. 2c, in which RTAmin and RTAmax are marked as the lower and upper limits of the arrival timeslot imposed by the ATM bodies of air traffic management, that is typically a few minutes before (for example 2 minutes before) and a few minutes after (for example 3 minutes after) the required time of arrival at destination RTA.
The cost of time differential ΔC of non-adherence then reflects the fact that the failure to maintain the required time of arrival at destination, that is to say when the aircraft arrives ahead of time, before RTAmin or late, after RTAmax, has effects on the management of the flight personnel, maintenance, or the expenses of diversion to another airport and the implications on the departure or arrival timeslots of other aircraft etc. These effects will often result in an increased operating cost (a positive cost differential) that is an increasing function of the delay.
But this component ΔC may also be negative, that is to say cause a reduction in the total cost of time. This will for example be the case if a flight 1 arrives late on its arrival timeslot after a time tmc (mc used to signify “missed connection”): the connection with a subsequent flight 2 which should normally have taken onboard passengers from flight 1, is missed: flight 2 leaves, in its normal timeslot. After this time tmc, the cost of non-adherence to the required timeslot will then sharply reduce but without descending to the cost with adherence to the timeslot (even if, in the long term, this has a negative economic impact for the company due to the discontent of the passengers left at the gate who will potentially choose another company for their future flights). This is illustrated by the curve ΔC as a function of the arrival time illustrated in FIG. 2c. 
The curve G(t) of the total cost of time (FIG. 2b), as a function of the flight time is in practice defined by an operator relative to its own management constraints, and relative to the constraints and limits of air traffic management (ATFCM: “Air Traffic Flow and Capacity Management”).
But the current flight management systems are not able to take account of the optimal cost index CI determined by the operator for a given mission, to generate a corresponding optimal flight plan with notably an estimate of the time on arrival and of the fuel remaining on arrival. Therefore, modifications of the flight plan during the mission that cause a non-adherence to the arrival timeslot may not be taken into account by these systems, which results on arrival in a real cost index CIr that is different from the optimal value CIopt determined by the operator.
According to the prior art, there are no tools onboard the aircraft that make it possible to make up the difference between the real cost index and the optimal cost index predetermined by the operator. And the flight management system has no means that could make it possible to return to the CT and CF indices from the CI. Therefore the crews onboard the aircraft do not have at their disposal tools making it possible to “make up” a difference of cost relative to the optimal cost index predetermined by the operator. They only have the difference in cost of fuel.